Due to slight Masonic jurisdictional differences around the world, this symbol does not always look exactly the same to all Freemasons.
Some jurisdictions call this symbol the Square and Compass, (non-plural) and a few jurisdictions omit the "G" at its center.
But, no matter its slightly different look, all Freemasons are in unison as to what this symbol means to them within the fraternity.
The Letter G stands for "Geometry", which is the mathematical science upon which Architecture and Masonry were founded.
No, the thing on the Steubenville logo is a stylized representation of the Veterans Memorial Bridge over the Ohio River. It doesn’t have anything to do with Freemasonry.